Pegging your currency to another currency and claiming it's more stable is cheating and doesn't really solve the problem.
Like the US can stop PayPal from providing financial services, they can too stop banks from storing USD collateral to such parties.
Also I don't agree with your "tracked better than that" claim: DAI/USD has a 15% drop and increase in a few months, about the same as USD/EUR in 5 years.
Consider USD/EUR. In 2015 it was 0.9, and currently it's 0.89. It's peak and low was 0.96 and 0.8. That a 10% bandwidth around a stable average.